Abstract

Integration of coordinated robotic table motion with inversely-planned arc delivery has the potential to resolve table-top delivery limitations of large-field treatments such as Total Body Irradiation (TBI), Total Lymphoid Irradiation (TLI), and Cranial-Spinal Irradiation (CSI). We formulate the foundation for Trajectory Modulated Arc Therapy (TMAT), and using Varian Developer Mode capabilities, experimentally investigate its practical implementation for such techniques.A MATLAB algorithm was developed for inverse planning optimization of the table motion, MLC positions, and gantry motion under extended-SSD geometry. To maximize the effective field size, delivery trajectories for TMAT TBI were formed with the table rotated at 270° IEC and dropped vertically to 152.5cm SSD. Preliminary testing of algorithm parameters was done through retrospective planning analysis. Robotic delivery was programmed using custom XML scripting on the TrueBeam Developer Mode platform. Final dose was calculated using the Eclipse AAA algorithm. Initial verification of delivery accuracy was measured using OSLDs on a solid water phantom of varying thickness.A comparison of DVH curves demonstrated that dynamic couch motion irradiation was sufficiently approximated by static control points spaced in intervals of less than 2cm. Optimized MLC motion decreased the average lung dose to 68.5% of the prescription dose. The programmed irradiation integrating coordinated table motion was deliverable on a TrueBeam STx linac in 6.7 min. With the couch translating under an open 10cmx20cm field angled at 10°, OSLD measurements along the midline of a solid water phantom at depths of 3, 5, and 9cm were within 3% of the TPS AAA algorithm with an average deviation of 1.2%.A treatment planning and delivery system for Trajectory Modulated Arc Therapy of extended volumes has been established and experimentally demonstrated for TBI. Extension to other treatment techniques such as TLI and CSI is readily achievable through the developed platform. Grant Funding by Varian Medical Systems.

Abstract

Purpose: To assess whether air scintillation produced during standard radiation treatments can be visualized and used to monitor a beam in a nonperturbing manner.Methods: Air scintillation is caused by the excitation of nitrogen gas by ionizing radiation. This weak emission occurs predominantly in the 300-430 nm range. An electron-multiplication charge-coupled device camera, outfitted with an f∕0.95 lens, was used to capture air scintillation produced by kilovoltage photon beams and megavoltage electron beams used in radiation therapy. The treatment rooms were prepared to block background light and a short-pass filter was utilized to block light above 440 nm.Results: Air scintillation from an orthovoltage unit (50 kVp, 30 mA) was visualized with a relatively short exposure time (10 s) and showed an inverse falloff (r(2) = 0.89). Electron beams were also imaged. For a fixed exposure time (100 s), air scintillation was proportional to dose rate (r(2) = 0.9998). As energy increased, the divergence of the electron beam decreased and the penumbra improved. By irradiating a transparent phantom, the authors also showed that Cherenkov luminescence did not interfere with the detection of air scintillation. In a final illustration of the capabilities of this new technique, the authors visualized air scintillation produced during a total skin irradiation treatment.Conclusions: Air scintillation can be measured to monitor a radiation beam in an inexpensive and nonperturbing manner. This physical phenomenon could be useful for dosimetry of therapeutic radiation beams or for online detection of gross errors during fractionated treatments.

Abstract

External beam radiation therapy (EBRT) provides a non-invasive treatment alternative for accelerated partial breast irradiation (APBI), however, limitations in achievable dose conformity of current EBRT techniques have been correlated to reported toxicity. To enhance the conformity of EBRT APBI, a technique for conventional LINACs is developed, which through combined motion of the couch, intensity modulated delivery, and a prone breast setup, enables wide-angular coronal arc irradiation of the ipsilateral breast without irradiating through the thorax and contralateral breast.A couch trajectory optimization technique was developed to determine the trajectories that concurrently avoid collision with the LINAC and maintain the target within the MLC apertures. Inverse treatment planning was performed along the derived trajectory. The technique was experimentally implemented by programming the Varian TrueBeam™ STx in Developer Mode. The dosimetric accuracy of the delivery was evaluated by ion chamber and film measurements in phantom.The resulting optimized trajectory was shown to be necessarily non-isocentric, and contain both translation and rotations of the couch. Film measurements resulted in 93% of the points in the measured two-dimensional dose maps passing the 3%/3mm Gamma criterion. Preliminary treatment plan comparison to 5-field 3D-conformal, IMRT, and VMAT demonstrated enhancement in conformity, and reduction of the normal tissue V50% and V100% parameters that have been correlated with EBRT toxicity.The feasibility of wide-angular intensity modulated partial breast irradiation using motion of the couch has been demonstrated experimentally on a standard LINAC for the first time. For patients eligible for a prone setup, the technique may enable improvement of dose conformity and associated dose-volume parameters correlated with toxicity.

Abstract

A Fourier-based iterative reconstruction technique, termed Equally Sloped Tomography (EST), is developed in conjunction with advanced mathematical regularization to investigate radiation dose reduction in x-ray CT. The method is experimentally implemented on fan-beam CT and evaluated as a function of imaging dose on a series of image quality phantoms and anonymous pediatric patient data sets. Numerical simulation experiments are also performed to explore the extension of EST to helical cone-beam geometry.EST is a Fourier based iterative algorithm, which iterates back and forth between real and Fourier space utilizing the algebraically exact pseudopolar fast Fourier transform (PPFFT). In each iteration, physical constraints and mathematical regularization are applied in real space, while the measured data are enforced in Fourier space. The algorithm is automatically terminated when a proposed termination criterion is met. Experimentally, fan-beam projections were acquired by the Siemens z-flying focal spot technology, and subsequently interleaved and rebinned to a pseudopolar grid. Image quality phantoms were scanned at systematically varied mAs settings, reconstructed by EST and conventional reconstruction methods such as filtered back projection (FBP), and quantified using metrics including resolution, signal-to-noise ratios (SNRs), and contrast-to-noise ratios (CNRs). Pediatric data sets were reconstructed at their original acquisition settings and additionally simulated to lower dose settings for comparison and evaluation of the potential for radiation dose reduction. Numerical experiments were conducted to quantify EST and other iterative methods in terms of image quality and computation time. The extension of EST to helical cone-beam CT was implemented by using the advanced single-slice rebinning (ASSR) method.Based on the phantom and pediatric patient fan-beam CT data, it is demonstrated that EST reconstructions with the lowest scanner flux setting of 39 mAs produce comparable image quality, resolution, and contrast relative to FBP with the 140 mAs flux setting. Compared to the algebraic reconstruction technique and the expectation maximization statistical reconstruction algorithm, a significant reduction in computation time is achieved with EST. Finally, numerical experiments on helical cone-beam CT data suggest that the combination of EST and ASSR produces reconstructions with higher image quality and lower noise than the Feldkamp Davis and Kress (FDK) method and the conventional ASSR approach.A Fourier-based iterative method has been applied to the reconstruction of fan-bean CT data with reduced x-ray fluence. This method incorporates advantageous features in both real and Fourier space iterative schemes: using a fast and algebraically exact method to calculate forward projection, enforcing the measured data in Fourier space, and applying physical constraints and flexible regularization in real space. Our results suggest that EST can be utilized for radiation dose reduction in x-ray CT via the readily implementable technique of lowering mAs settings. Numerical experiments further indicate that EST requires less computation time than several other iterative algorithms and can, in principle, be extended to helical cone-beam geometry in combination with the ASSR method.

Abstract

X-ray scatter incurred to detectors degrades the quality of cone-beam computed tomography (CBCT) and represents a problem in volumetric image guided and adaptive radiation therapy. Several methods using a beam blocker for the estimation and subtraction of scatter have been proposed. However, due to missing information resulting from the obstruction of the blocker, such methods require dual scanning or dynamically moving blocker to obtain a complete volumetric image. Here, we propose a half beam blocker-based approach, in conjunction with a total variation (TV) regularized Feldkamp-Davis-Kress (FDK) algorithm, to correct scatter-induced artifacts by simultaneously acquiring image and scatter information from a single-rotation CBCT scan.A half beam blocker, comprising lead strips, is used to simultaneously acquire image data on one side of the projection data and scatter data on the other half side. One-dimensional cubic B-Spline interpolation/extrapolation is applied to derive patient specific scatter information by using the scatter distributions on strips. The estimated scatter is subtracted from the projection image acquired at the opposite view. With scatter-corrected projections where this subtraction is completed, the FDK algorithm based on a cosine weighting function is performed to reconstruct CBCT volume. To suppress the noise in the reconstructed CBCT images produced by geometric errors between two opposed projections and interpolated scatter information, total variation regularization is applied by a minimization using a steepest gradient descent optimization method. The experimental studies using Catphan504 and anthropomorphic phantoms were carried out to evaluate the performance of the proposed scheme.The scatter-induced shading artifacts were markedly suppressed in CBCT using the proposed scheme. Compared with CBCT without a blocker, the nonuniformity value was reduced from 39.3% to 3.1%. The root mean square error relative to values inside the regions of interest selected from a benchmark scatter free image was reduced from 50 to 11.3. The TV regularization also led to a better contrast-to-noise ratio.An asymmetric half beam blocker-based FDK acquisition and reconstruction technique has been established. The proposed scheme enables simultaneous detection of patient specific scatter and complete volumetric CBCT reconstruction without additional requirements such as prior images, dual scans, or moving strips.

Abstract

Tomographic reconstruction from undersampled and noisy projections is often desirable in transmission CT modalities for purposes of low-dose tomography and fast acquisition imaging. However under such conditions, due to the violation of the Nyquist sampling criteria and the presence of noise, reconstructions with acceptable accuracy may not be possible. Recent experiments in transmission electron tomography and coherent diffraction microscopy have shown that the technique of equally sloped tomography (EST), an exact tomographic method utilizing an oversampling iterative Fourier-based reconstruction, provides more accurate image reconstructions when the number of projections is significantly undersampled relative to filtered back projection and algebraic iterative methods. Here we extend this technique by developing new reconstruction algorithms which allow for the incorporation of advanced mathematical regularization constraints, such as the nonlocal means total variational model, in a manner that is consistent with experimental projections. We then evaluate the resulting image quality of the developed algorithm through simulations and experiments at the European Synchrotron Radiation Facility on image quality phantoms using the x-ray absorption and phase contrast CT modalities. Both our simulation and experimental results have indicated that the method can reduce the number of projections by 60-75% in parallel beam modalities, while achieving comparable or better image quality than the conventional reconstructions. As large-scale and compact synchrotron radiation facilities are currently under rapid development worldwide, the implementation of low-dose x-ray absorption and phase-contrast CT can find broad applications in biology and medicine using these advanced x-ray sources.

Abstract

The first stereotactic arrhythmia radioablation (STAR) of ventricular tachycardia (VT) was delivered at Stanford on a robotic radiosurgery system (CyberKnife® G4) in 2012. The results warranted further investigation of this treatment. Here we compare dosimetrically three possible treatment delivery platforms for STAR.The anatomy and target volume of the first treated patient were used for this study. A dose of 25 Gy in one fraction was prescribed to the planning target volume (PTV). Treatment plans were created on three treatment platforms: CyberKnife® G4 system with Iris collimator (Multiplan, V. 4.6)(Plan #1), CyberKnife® M6 system with InCise 2(TM) multileaf collimator (Multiplan V. 5.3)(Plan #2) and Varian TrueBeam(TM) STx with HD 120(TM) MLC and 10MV flattening filter free (FFF) beam (Eclipse planning system, V.11) (Plan #3 coplanar and #4 noncoplanar VMAT plans). The four plans were compared by prescription isodose line, plan conformity index, dose gradient, as well as dose to the nearby critical structures. To assess the delivery efficiency, planned monitor units (MU) and estimated treatment time were evaluated.Plans #1-4 delivered 25 Gy to the PTV to the 75.0%, 83.0%, 84.3%, and 84.9% isodose lines and with conformity indices of 1.19, 1.16, 1.05, and 1.05, respectively. The dose gradients for plans #1-4 were 3.62, 3.42, 3.93, and 3.73 with the CyberKnife® MLC plan (Plan #2) the best, and the TrueBeam(TM) STx co-planar plan (Plan #3) the worst. The dose to nearby critical structures (lung, stomach, bowel, and esophagus) were all well within tolerance. The MUs for plans #1-4 were 27671, 16522, 6275, and 6004 for an estimated total-treatment-time/beam-delivery-time of 99/69, 65/35, 37/7, and 56/6 minutes, respectively, under the assumption of 30 minutes pretreatment setup time. For VMAT gated delivery, a 40% duty cycle, 2400MU/minute dose rate, and an extra 10 minutes per extra arc were assumed.Clinically acceptable plans were created with all three platforms. Plans with MLC were considerably more efficient in MU. CyberKnife® M6 with InCise 2(TM) collimator provided the most conformal plan (steepest dose drop-off) with significantly reduced MU and treatment time. VMAT plans were most efficient in MU and delivery time. Fluoroscopic image guidance removes the need for additional fiducial marker placement; however, benefits may be moderated by worse dose gradient and more operator-dependent motion management by gated delivery.

Abstract

To investigate a miniature optical dosimeter for real-time, high-resolution dosimetry, and explore its potential applications for in vivo measurements and small field dosimetry.A micro-sized hemispherical (400 µm radius) scintillating detector was constructed from lanthanide activated phosphors doped with Europium (GOS:Eu) and encapsulated in a 17 gauge plastic catheter. A photon counting PMT and CCD-chip spectrometer were used to detect signals emitted from the detector. A single band-passing spectral approach (630nm) was implemented to discriminate the micro-phosphor optical signal from background signals (Cerenkov radiation) in the optical fiber. To test real-time monitoring capabilities, a 3D-printed phantom was used to detect an 192Ir HDR brachytherapy source at locations ranging from 1 to 4 cm radially and 12 cm along the travel axis of the HDR wire. To test the application of the micro-sized detector for small field dosimetry, the linearity of detector was characterized through irradiation of 6MV photon beam at dose-rates ranging from 100 to 600 MU, and the effect of field size was characterized through detections of beams ranging from 30×30 to 1×1 cm2 size.With a 1 second integration time for the spectrometer, the recorded measurements indicated that the micro-sized detector allowed accurate detection of source position at distances of up to 6 cm along the axis of travel in water. EB measurements showed that the detected signal was linearly correlated with dose rate (R^2 = 0.99). The crossbeam profile was determined with a step size of ∼500 µm.Miniaturization of optical dosimeters is shown to be possible through the construction of lanthanide activated doped phosphors detectors. The small size of the detector makes it amenable to a variety of applications, including real-time dose delivery verification during HDR brachytherapy and EB beam calibrations in small fields.

Abstract

Intrafraction target motion is a prominent complicating factor in the accurate targeting of radiation within the body. Methods compensating for target motion during treatment, such as gating and dynamic tumor tracking, depend on the delineation of target location as a function of time during delivery. A variety of techniques for target localization have been explored and are under active development; these include beam-level imaging of radio-opaque fiducials, fiducial-less tracking of anatomical landmarks, tracking of electromagnetic transponders, optical imaging of correlated surrogates, and volumetric imaging within treatment delivery. The Joint Imaging and Therapy Symposium will provide an overview of the techniques for real-time imaging and tracking, with special focus on emerging modes of implementation across different modalities. In particular, the symposium will explore developments in 1) Beam-level kilovoltage X-ray imaging techniques, 2) EPID-based megavoltage X-ray tracking, 3) Dynamic tracking using electromagnetic transponders, and 4) MRI-based soft-tissue tracking during radiation delivery.1.Understand the fundamentals of real-time imaging and tracking techniques2.Learn about emerging techniques in the field of real-time tracking3.Distinguish between the advantages and disadvantages of different tracking modalities4.Understand the role of real-time tracking techniques within the clinical delivery work-flow.

Abstract

The advent of electromagnetic navigation bronchoscopy has enabled minimally invasive access to peripheral lung tumors previously inaccessible by optical bronchoscopes. As an adjunct to Stereotactic Ablative Radiosurgery (SABR), implantation of HDR catheters can provide focal treatments for multiple metastases and sites of retreatments. The authors evaluate a procedure to deliver ablative doses via Electromagnetically-Guided HDR (EMG-HDR) to lung metastases, quantify the resulting dosimetry, and assess its role in the comprehensive treatment of lung cancer.A retrospective study was conducted on ten patients, who, from 2009 to 2011, received a hypo-fractionated SABR regimen with 6MV VMAT to lesions in various lobes ranging from 1.5 to 20 cc in volume. A CT visible pathway was delineated for EM guided placement of an HDR applicator (catheter) and dwell times were optimized to ensure at least 98% prescription dose coverage of the GTV. Normal tissue doses were calculated using inhomogeneity corrections via a grid-based Boltzmann solver (Acuros_BV_1.5.0).With EMG-HDR, an average of 83% (+/-9% standard deviation) of each patient's GTV received over 200% of the prescription dose, as compared to SABR where the patients received an average maximum dose of 125% (+/-5%). EMG-HDR enabled a 59% (+/-12%) decrease in the aorta maximum dose, a 63% (+/-26%) decrease in the spinal cord max dose, and 57% (+/-23%) and 70% (+/-17%) decreases in the volume of the body receiving over 50% and 25% of the prescription dose, respectively.EMG-HDR enables delivery of higher ablative doses to the GTV, while concurrently reducing surrounding normal tissue doses. The single catheter approach shown here is limited to targets smaller than 20 cc. As such, the technique enables ablation of small lesions and a potentially safe and effective retreatment option in situations where external beam utility is limited by normal tissue constraints.

Abstract

In this study, the authors introduce and demonstrate quality control procedures for evaluating the geometric and dosimetric fidelity of dynamic treatment delivery techniques involving treatment couch motion synchronous with gantry and multileaf collimator (MLC). Tests were designed to evaluate positional accuracy, velocity constancy and accuracy for dynamic couch motion under a realistic weight load. A test evaluating the geometric accuracy of the system in delivering treatments over complex dynamic trajectories was also devised. Custom XML scripts that control the Varian TrueBeam™ STx (Serial #3) axes in Developer Mode were written to implement the delivery sequences for the tests. Delivered dose patterns were captured with radiographic film or the electronic portal imaging device. The couch translational accuracy in dynamic treatment mode was 0.01 cm. Rotational accuracy was within 0.3°, with 0.04 cm displacement of the rotational axis. Dose intensity profiles capturing the velocity constancy and accuracy for translations and rotation exhibited standard deviation and maximum deviations below 3%. For complex delivery involving MLC and couch motions, the overall translational accuracy for reproducing programmed patterns was within 0.06 cm. The authors conclude that in Developer Mode, TrueBeam™ is capable of delivering dynamic treatment delivery techniques involving couch motion with good geometric and dosimetric fidelity.

Abstract

Gated Volumetric Modulated Arc Therapy (VMAT) is an emerging radiation therapy modality for treatment of tumors affected by respiratory motion. However, gating significantly prolongs the treatment time, as delivery is only activated during a single respiratory phase. To enhance the efficiency of gated VMAT delivery, a novel dual-gated VMAT (DG-VMAT) technique, in which delivery is executed at both exhale and inhale phases in a given arc rotation, is developed and experimentally evaluated.Arc delivery at two phases is realized by sequentially interleaving control points consisting of MUs, MLC sequences, and angles of VMAT plans generated at the exhale and inhale phases. Dual-gated delivery is initiated when a respiration gating signal enters the exhale window; when the exhale delivery concludes, the beam turns off and the gantry rolls back to the starting position for the inhale window. The process is then repeated until both inhale and exhale arcs are fully delivered. DG-VMAT plan delivery accuracy was assessed using a pinpoint chamber and diode array phantom undergoing programmed motion.DG-VMAT delivery was experimentally implemented through custom XML scripting in Varian's TrueBeam™ STx Developer Mode. Relative to single gated delivery at exhale, the treatment time was improved by 95.5% for a sinusoidal breathing pattern. The pinpoint chamber dose measurement agreed with the calculated dose within 0.7%. For the DG-VMAT delivery, 97.5% of the diode array measurements passed the 3%/3 mm gamma criterion.The feasibility of DG-VMAT delivery scheme has been experimentally demonstrated for the first time. By leveraging the stability and natural pauses that occur at end-inspiration and end-exhalation, DG-VMAT provides a practical method for enhancing gated delivery efficiency by up to a factor of two.

Abstract

In four-dimensional (4D) cone-beam computed tomography (CBCT), there is a spatio-temporal tradeoff that currently limits the accuracy. The aim of this study is to develop a Bregman iteration based formalism for high quality 4D CBCT image reconstruction from a limited number of low-dose projections. The 4D CBCT problem is first divided into multiple 3D CBCT subproblems by grouping the projection images corresponding to the phases. To maximally utilize the information from the under-sampled projection data, a compressed sensing (CS) method with Bregman iterations is employed for solving each subproblem. We formulate an unconstrained optimization problem based on least-square criterion regularized by total-variation. The least-square criterion reflects the inconsistency between the measured and the estimated line integrals. Furthermore, the unconstrained problem is updated and solved repeatedly by Bregman iterations. The performance of the proposed algorithm is demonstrated through a series of simulation studies and phantom experiments, and the results are compared to those of previously implemented compressed sensing technique using other gradient-based methods as well as conventional filtered back-projection (FBP) results. The simulation and experimental studies have shown that artifact suppressed images can be obtained with as small as 41 projections per phase, which is adequate for clinical 4D CBCT reconstruction. With such small number of projections, the conventional FDK failed to yield meaningful 4D CBCT images, and CS technique using conjugate gradient was not able to recover sharp edges. The proposed method significantly reduces the radiation dose and scanning time to achieve the high quality images compared to the 4D CBCT imaging based on the conventional FDK technique and the existing CS techniques.

Abstract

Monoscopic x-ray imaging with on-board kV devices is an attractive approach for real-time image guidance in modern radiation therapy such as VMAT or IMRT, but it falls short in providing reliable information along the direction of imaging x-ray. By effectively taking consideration of projection data at prior times and/or angles through a Bayesian formalism, the authors develop an algorithm for real-time and full 3D tumor localization with a single x-ray imager during treatment delivery.First, a prior probability density function is constructed using the 2D tumor locations on the projection images acquired during patient setup. Whenever an x-ray image is acquired during the treatment delivery, the corresponding 2D tumor location on the imager is used to update the likelihood function. The unresolved third dimension is obtained by maximizing the posterior probability distribution. The algorithm can also be used in a retrospective fashion when all the projection images during the treatment delivery are used for 3D localization purposes. The algorithm does not involve complex optimization of any model parameter and therefore can be used in a "plug-and-play" fashion. The authors validated the algorithm using (1) simulated 3D linear and elliptic motion and (2) 3D tumor motion trajectories of a lung and a pancreas patient reproduced by a physical phantom. Continuous kV images were acquired over a full gantry rotation with the Varian TrueBeam on-board imaging system. Three scenarios were considered: fluoroscopic setup, cone beam CT setup, and retrospective analysis.For the simulation study, the RMS 3D localization error is 1.2 and 2.4 mm for the linear and elliptic motions, respectively. For the phantom experiments, the 3D localization error is < 1 mm on average and < 1.5 mm at 95th percentile in the lung and pancreas cases for all three scenarios. The difference in 3D localization error for different scenarios is small and is not statistically significant.The proposed algorithm eliminates the need for any population based model parameters in monoscopic image guided radiotherapy and allows accurate and real-time 3D tumor localization on current standard LINACs with a single x-ray imager.

Abstract

Microscopy has greatly advanced our understanding of biology. Although significant progress has recently been made in optical microscopy to break the diffraction-limit barrier, reliance of such techniques on fluorescent labeling technologies prohibits quantitative 3D imaging of the entire contents of cells. Cryoelectron microscopy can image pleomorphic structures at a resolution of 3-5 nm, but is only applicable to thin or sectioned specimens. Here, we report quantitative 3D imaging of a whole, unstained cell at a resolution of 50-60 nm by X-ray diffraction microscopy. We identified the 3D morphology and structure of cellular organelles including cell wall, vacuole, endoplasmic reticulum, mitochondria, granules, nucleus, and nucleolus inside a yeast spore cell. Furthermore, we observed a 3D structure protruding from the reconstructed yeast spore, suggesting the spore germination process. Using cryogenic technologies, a 3D resolution of 5-10 nm should be achievable by X-ray diffraction microscopy. This work hence paves a way for quantitative 3D imaging of a wide range of biological specimens at nanometer-scale resolutions that are too thick for electron microscopy.

Abstract

We develop two new algorithms for tomographic reconstruction which incorporate the technique of equally-sloped tomography (EST) and allow for the optimized and flexible implementation of regularization schemes, such as total variation constraints, and the incorporation of arbitrary physical constraints. The founding structure of the developed algorithms is EST, a technique of tomographic acquisition and reconstruction first proposed by Miao in 2005 for performing tomographic image reconstructions from a limited number of noisy projections in an accurate manner by avoiding direct interpolations. EST has recently been successfully applied to coherent diffraction microscopy, electron microscopy, and computed tomography for image enhancement and radiation dose reduction. However, the bottleneck of EST lies in its slow speed due to its higher computation requirements. In this paper, we formulate the EST approach as a constrained problem and subsequently transform it into a series of linear problems, which can be accurately solved by the operator splitting method. Based on these mathematical formulations, we develop two iterative algorithms for tomographic image reconstructions through EST, which incorporate Bregman and continuative regularization. Our numerical experiment results indicate that the new tomographic image reconstruction algorithms not only significantly reduce the computational time, but also improve the image quality. We anticipate that EST coupled with the novel iterative algorithms will find broad applications in X-ray tomography, electron microscopy, coherent diffraction microscopy, and other tomography fields.

Abstract

The ability to determine the structure of matter in three dimensions has profoundly advanced our understanding of nature. Traditionally, the most widely used schemes for three-dimensional (3D) structure determination of an object are implemented by acquiring multiple measurements over various sample orientations, as in the case of crystallography and tomography, or by scanning a series of thin sections through the sample, as in confocal microscopy. Here we present a 3D imaging modality, termed ankylography (derived from the Greek words ankylos meaning 'curved' and graphein meaning 'writing'), which under certain circumstances enables complete 3D structure determination from a single exposure using a monochromatic incident beam. We demonstrate that when the diffraction pattern of a finite object is sampled at a sufficiently fine scale on the Ewald sphere, the 3D structure of the object is in principle determined by the 2D spherical pattern. We confirm the theoretical analysis by performing 3D numerical reconstructions of a sodium silicate glass structure at 2 A resolution, and a single poliovirus at 2-3 nm resolution, from 2D spherical diffraction patterns alone. Using diffraction data from a soft X-ray laser, we also provide a preliminary demonstration that ankylography is experimentally feasible by obtaining a 3D image of a test object from a single 2D diffraction pattern. With further development, this approach of obtaining complete 3D structure information from a single view could find broad applications in the physical and life sciences.

Abstract

Electron tomography is currently the highest resolution imaging modality available to study the 3D structures of pleomorphic macromolecular assemblies, viruses, organelles and cells. Unfortunately, the resolution is currently limited to 3-5nm by several factors including the dose tolerance of biological specimens and the inaccessibility of certain tilt angles. Here we report the first experimental demonstration of equally-sloped tomography (EST) to alleviate these problems. As a proof of principle, we applied EST to reconstructing frozen-hydrated keyhole limpet hemocyanin molecules from a tilt-series taken with constant slope increments. In comparison with weighted back-projection (WBP), the algebraic reconstruction technique (ART) and the simultaneous algebraic reconstruction technique (SART), EST reconstructions exhibited higher contrast, less peripheral noise, more easily detectable molecular boundaries and reduced missing wedge effects. More importantly, EST reconstructions including only two-thirds the original images appeared to have the same resolution as full WBP reconstructions, suggesting that EST can either reduce the dose required to reach a given resolution or allow higher resolutions to be achieved with a given dose. EST was also applied to reconstructing a frozen-hydrated bacterial cell from a tilt-series taken with constant angular increments. The results confirmed similar benefits when standard tilts are utilized.